2022ApJ...940...50C

With respect to the Hβ FWHM (FWHM_Hβ), the broad Hβ line dispersion (σ_Hβ) was preferred as a velocity tracer to calculate the single-epoch supermassive black hole mass (M_BH) suggested by Yu et al. For a compiled sample of 311 broad-line active galactic nuclei (AGNs) with measured hard X-ray photon index (z < 0.7), σ_Hβ and the optical Fe II relative strength (R_Fe) are measured from their optical spectra, which are used to calculate σ_Hβ-based virial M_BH and dimensionless accretion rate ($\dot{M}$). With respect to FWHM_Hβ, it is found that the mean value of σ_Hβ-based M_BH is on average larger by 0.26 dex and the mean value of σ_Hβ-based $\dot{M}$ is on average smaller by 0.51 dex. It is found that there exists a nonlinear relationship between the Eddington ratio (L_Bol/L_Edd) and $\dot{M}$, i.e., ${L}_{\mathrm{Bol}}/{L}_{\mathrm{Edd}}\propto {\dot{M}}^{0.56\pm 0.01}$. This nonlinear relationship comes from the accretion efficiency η, which is smaller for AGNs with higher $\dot{M}$. We find a strong bivariate correlation of the fraction of energy released in the corona F_X with $\dot{M}$ and M_BH, ${F}_{{\rm{X}}}\propto {\dot{M}}^{-0.57\pm 0.05}{M}_{\mathrm{BH}}^{-0.54\pm 0.06}$. The flat slope of -0.57 ± 0.05 favors the shear stress tensor of the accretion disk being proportional to the geometric mean of gas pressure and total pressure. We find a strong bivariate relation of Γ with $\dot{M}$ and F_X, ${\rm{\Gamma }}\propto {\dot{M}}^{-0.21\pm 0.02}{F}_{{\rm{X}}}^{0.02\pm 0.04}$. The hard X-ray spectrum becomes softer with increasing F_X, although the scatter is large.